Question:
In \(\triangle ABC\), if the line joining the circumcentre and incentre is parallel to \(BC\), then find \( \cos B + \cos C \).
In \(\triangle ABC\), if the line joining the circumcentre and incentre is parallel to \(BC\), then find \( \cos B + \cos C \).
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Recall properties of triangle centers (circumcentre, incentre) and their relations to side angles for parallel line conditions.
Updated On: Jun 6, 2025
- \(\frac{1}{2}\)
- \(\frac{3}{4}\)
- \(1\)
- \(\frac{3}{2}\)
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The Correct Option is C
Solution and Explanation
If the line joining the circumcentre \(O\) and incentre \(I\) is parallel to side \(BC\), then by properties of triangle centers,
\[
\cos B + \cos C = 1.
\]
This is a known geometric property that arises from the configuration of centers in the triangle and their relative alignments.
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